This invention relates generally to techniques for measuring electrical conductance, and more particularly relates to the measurement of electrical conductance in thin solid state materials and structures.
The measurement of electrical conductance has become an important technique for characterizing solid state systems. For example, the examination of the dependence of the electrical resistance of a solid state system, as indicated by measured electrical conductance, on external variables such as temperature, electrical and magnetic fields, and light exposure, has enabled intimate probing of novel solid state physics effects. Beyond such analysis of particular external stimuli on a given system, electrical characterization is required in general of new materials and structures to enable their reliable implementation in a wide range of microelectronic, biological, and chemical applications.
For many microscale and nanoscale materials and structures, the measurement of electrical conductance is not straightforward. For example, effects can be introduced by electrically conducting contact pads that are located at the site of a given material or structure for making electrical contact to the material or structure under measurement. The contact resistance of such electrical contact pads, i.e., the electrical resistance of the interface between the electrically conducting material forming the contact pads and the material under measurement, as opposed to the intrinsic resistance of the material or structure under measurement, can for many configurations dominate the overall resistance of a micro-device system or other micro-scale structure, over the intrinsic resistance of a material or structure in the system that is under measurement.
As a result, contact resistance can limit the operation as well as characterization of micro-scale systems. For example, for nanometric structures, the area of electrical contact is correspondingly small, producing an increased contact resistance. Because a nanometric channel length is correspondingly short, the resistance of a nanometric channel is relatively low. As a result, as the as device sizes are reduced, contact resistance can begin to dominate the overall resistance of a nanometric field effect structure. For example, in graphene electronics, the metal-graphene interface at contact pads, and the resistance associated with this interface has limited the ability to produce high-performance graphene transistors. In organic electronics, contact pad material has been found to form a Schottky barrier with an organic material due to, e.g., damage of or penetration into the organic material, producing a resistive interface that introduces a voltage drop, irrespective of work function. As a result, the measured electrical resistance of, e.g., an organic monolayer, can vary by four orders of magnitude, depending on the choice of contact material and the method of contact with the material. Further, it is found that as charge mobility is increased in novel organic materials, contact effects and Schottky barriers become more pronounced. Schottky barriers between contact pads and a material under analysis have long been obstacles to the characterization of semiconductor films, and as novel semiconducting materials are developed, it can be difficult to discern the effect of contacts on the material measurements.
One technique for eliminating contact resistance effects from an electrical conductance measurement is a four-point probe measurement, in which separate pairs of electrical current-carrying and voltage-sensing electrodes are employed to eliminate the contribution of contact resistance to measurement of impedance. As materials and structures evolve to the nanoscale, four-point probes are found to be incompatible with electrical measurement, however. For example, four point probes can interfere with current flow, e.g., in nanoscale films, and can damage soft, organic nanoscale materials and biological structures. Conventional electrical measurement techniques are therefore found to be increasingly inadequate for characterization of microscale and nanoscale materials and systems.